1) Telling someone only affects future assignments and FITREP ranking. It wouldn't affect your ability to receive an honorable discharge and severance pay if you stay that route. If it did, you would have grounds for a grievance.
2) Sign up for TAP when you have separation orders in hand.
3) Dropping your letter would make you ineligible for severance pay. You would only receive that as a service directed reduction in force, twice failing to screen for the next higher rank while ineligible for retirement, or other rare occurrences.
4) Yes. See above.
5) When you are 6-12 months out from separation.
6) Yes.
7) No. Voluntarily leaving the service after taking a retention bonus obligates you to paying it back.
Good luck!